Problem: I have 5 red plates and 4 blue plates. If I randomly select two plates to serve dinner on, what is the probability that they're both the same color?
Answer: There are ${9 \choose 2} = 36$ pairs of plates possible in all. Exactly ${5 \choose 2} = 10$ of these pairs are both red plates and $\binom{4}{2}=6$ pairs are both blue plates for a total of $6+10=16$ pairs of plates that satisfy our condition. So, the probability of the pair of plates being the same color is $\frac{16}{36}=\boxed{\frac{4}{9}}$.